Taylors-theorem

Question

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001.

Answer 1

Step 1:

The function .

Taylors theorem:

If a function is differentiable through order in an interval containing , then for each in , there exist between and such that , ,

where error .

Here and .

From the Taylor polynomial it is fifth degree polynomial.

Determine by substituting corresponding values in .

Substitute in .

Step 2:

Error

The error cannot exceed 0.001 implies that .

Solution:

The value of is lies between .